Liouville property and quasi-isometries on non-positively curved Riemannian surfaces

Abstract

Kanai proved the stability under quasi-isometries of several global properties for Riemannian manifolds with the restriction of having positive injectivity radius. This work shows the stability of the Liouville property for Riemannian surfaces with non-positive curvature, where the restriction on the injectivity radius has been removed.